Investigators are close to pinning the murder of the fourth Gilgo Beach victim on suspected serial killer Rex Heuermann — and are widening their probe to connect him to the other six bodies dumped in the remote Long Island spot, a law enforcement source told The Post.

The latest update on the case comes after Heuermann was charged last week with killing three petite sex workers — Melissa Barthelemy, 24, Megan Waterman, 22, and Amber Lynn Costello, 27 — whose remains were found in 2010. 

The women, along with Maureen Brainard-Barnes, 25, were known as the “Gilgo Four.” Heuermann pleaded not guilty to three counts each of first- and second-degree murder.

He is considered the prime suspect in Brainard-Barnes’ death, officials have said.

“Now that we’ve brought prosecution on three of the murders, and we believe we’re going to be very close to resolving the fourth one very soon, we are going to continue on into all those other cases,” the source said.

At the same time, investigators weren’t sure if any of the women were killed in Heuermann’s Massapequa Park home but were pouring through mounds of evidence looking for their DNA or other evidence, the source said.

“That’s why we are doing the searches that we’re doing,” the source said. “It’s going to take months of testing before we even know if we found anything because, you know, it could be Rex’s blood, it could be a victim’s blood, it could be ketchup.”

As far as connecting his DNA to crimes nationally, the source said, Heuermann’s DNA will be put through the FBI’s database only if and when he is convicted.

Police can compare his DNA to that found in similar crimes elsewhere.

Meanwhile, investigators are moving through a list of hundreds of people they want to talk to – from women he met on the Internet to coworkers, pimps, and “anyone who was in contact with him.”

At the alleged killer’s home, Suffolk County Police Commissioner Rodney Harrison said investigators found some items they needed “to take a closer look at,” but refused to provide specifics.

“There’s a lot of junk in the house,” he added.

Investigators have been seen pulling a blond doll wearing a red dress encased in a wooden cabinet out of the home.

They’ve also removed a Playboy magazine, film negatives, a poster from the TV show “M*A*S*H,” and a macabre painting of a woman with a battered face.

Cops swooped in and arrested Heuermann July 13 outside of his Midtown architecture office sooner than they planned, out of fear for the safety of other possible victims and because of secrecy concerns as they questioned more and more people, Suffolk County District Attorney Raymond Tierney told The Post.

The remains of 10 people, including a little girl and a young man dressed as a woman, were found in the Gilgo Beach area. Investigators are looking at all of the cases, Tierney said.

“But now that we’ve done that we’re going to continue to prepare the three cases for trial, work on the fourth…and then expand the investigation to the other incidents as well,” said Tierney, who’s been described as a “working DA” because of the hours he put in on cases.  

“This is just the beginning,” Tierney said. “It’s about the victims. It’s about the community having faith in law enforcement.”